호남수학학술지 (Honam Mathematical Journal)

  • 제36권1호
  • /
  • Pages.103-112
  • /
  • 2014
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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THE REPRESENTATION OF THE GOLDEN RATIO BY THE CONTINUED FRACTION

  • Kim, Seung Soo (Department of Mathematics (Institute of Pure and Applied Mathematics), Chonbuk National University) ;
  • Ko, Mi Yeon (Department of Mathematics Educations, Graduate School, Chonbuk National University) ;
  • Lee, Yong Hun (Department of Mathematics (Institute of Pure and Applied Mathematics), Chonbuk National University)
  • 투고 : 2013.12.02
  • 심사 : 2014.01.15
  • 발행 : 2014.03.25
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초록

There are several theories to say that 'Mathematics is beautiful', but the typical one of them is a theory about the golden ratio. Often the golden ratio apt to be considered only as the geometric shapes or the simple number of ratio used in buildings and arts. However in this paper, we studied to consider the mathematical theories which are contained in their inside. In particular, we investigate the various expressions of the continued fraction which are represented by the golden ratio.

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참고문헌

  1. R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, 3rd Ed., JOHN WILEY & SON, 2000.
  2. James F. Epperson, An Introduction to Numerical Methods and Analysis, JOHN WILEY & SON, INC 2002.
  3. A. Y. Khinchin, Continued fractions, Dover Publications, inc., 1997.
  4. S. L. Griffing, The Golden Section : An Ancient Egyptian and Grecian Proportion, Xlibris Corporation, 1998.